Question

How can you connect two resistors so that a)maximum and b)minimum current flows in the electric circuit? Explain why you connected them in that particular manner

Answer 1

Consider two resistors of resistance R 1 and R 2 respectively

Let R 1=R 2= R

There are only two ways in which these two resistors can be connected

• series
• parallel

Series:

Let us connect two resistors of resistance R 1 and R 2 each of resistance R in series combination

Equivalent resistance for two resistances connected in series

$\rightarrow \mathtt{R _s = R 1 + R 2 }$

$\rightarrow \mathtt{R _s= R + R}$

$\rightarrow \mathtt{R _s =2 R}$

Let the voltage of the battery be V

So the current flowing through the circuit will be given by

$\rightarrow \mathtt{I_s = \dfrac{V }{R_s} }$

Now substituting the value of R in the above equation we get,

$\rightarrow \mathtt{I_s = \dfrac{V }{2R} }$

Substituting V/R as I in the above equation we get ,

$\rightarrow \mathtt{I_s = \dfrac{ I}{2} }$

hence from this we can conclude that ,

when two resistors are connected in series combination the net equivalent resistance is maximum and the current flowing through the combination will be minimum as current is inversely proportional to resistance

Parallel:

Let us connect two resistors of resistance R 1 and R 2 each of resistance R in parallel combination

Equivalent resistance for two resistances connected in parallel

$\rightarrow \mathtt{ \dfrac{1}{Rp} = \dfrac{1}{R1} + \dfrac{1}{R2} }$

$\rightarrow \mathtt{ \dfrac{1}{Rp} = \dfrac{1}{R} + \dfrac{1}{R} }$

$\rightarrow \mathtt{ Rp = \dfrac{R}{2} }$

Let the voltage of the battery be V

So the current flowing through the circuit will be given by

$\rightarrow \mathtt{I_p = \dfrac{V }{R_p} }$

$\rightarrow \mathtt{I_p = \dfrac{2V }{R} }$

Substituting V/R as I in the above equation we get ,

$\rightarrow \mathtt{I_p = 2 I }$

hence from this we can conclude that ,

when two resistors are connected in parallel combination the net equivalent resistance is minimum and the current flowing through the combination will be maximum as current is inversely proportional to resistance